The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
John Lygeros - One of the best experts on this subject based on the ideXlab platform.
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a Scenario Approach for non convex control design
IEEE Transactions on Automatic Control, 2016Co-Authors: Sergio Grammatico, Kostas Margellos, Xiaojing Zhang, Paul J Goulart, John LygerosAbstract:Randomized optimization is an established tool for control design with modulated robustness. While for uncertain convex programs there exist efficient randomized Approaches, this is not the case for non-convex problems. Methods based on statistical learning theory are applicable to non-convex problems, but they usually are conservative in achieving the desired probabilistic guarantees. In this paper, we derive a novel Scenario Approach for a wide class of random non-convex programs, with a sample complexity similar to that of uncertain convex programs and with probabilistic guarantees that hold not only for the optimal solution of the Scenario program, but for all feasible solutions inside a set of a-priori chosen complexity. We also address measure-theoretic issues for uncertain convex and non-convex programs. Among the family of non-convex control-design problems that can be addressed via randomization, we apply our Scenario Approach to stochastic model predictive control for chance constrained nonlinear control-affine systems.
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on the sample size of random convex programs with structured dependence on the uncertainty
Automatica, 2015Co-Authors: Xiaojing Zhang, Sergio Grammatico, Paul J Goulart, Georg Schildbach, John LygerosAbstract:The “Scenario Approach” provides an intuitive method to address chance constrained problems arising in control design for uncertain systems. It addresses these problems by replacing the chance constraint with a finite number of sampled constraints (Scenarios). The sample size critically depends on Helly’s dimension, a quantity always upper bounded by the number of decision variables. However, this standard bound can lead to computationally expensive programs whose solutions are conservative in terms of cost and violation probability. We derive improved bounds of Helly’s dimension for problems where the chance constraint has certain structural properties. The improved bounds lower the number of Scenarios required for these problems, leading both to improved objective value and reduced computational complexity. Our results are generally applicable to Randomized Model Predictive Control of chance constrained linear systems with additive uncertainty and affine disturbance feedback.
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on the sample size of random convex programs with structured dependence on the uncertainty
arXiv: Optimization and Control, 2015Co-Authors: Xiaojing Zhang, Sergio Grammatico, Paul J Goulart, Georg Schildbach, John LygerosAbstract:Many control design problems subject to uncertainty can be cast as chance constrained optimization programs. The Scenario Approach provides an intuitive way to address these problems by replacing the chance constraint with a finite number of sampled constraints (Scenarios). The sample size critically depends on the so-called Helly's dimension, which is always upper bounded by the number of decision variables. However, this standard bound can lead to computationally expensive programs whose solutions are conservative in terms of cost/violation probability. This paper derives improved bounds of Helly's dimension for problems where the chance constraint has certain structural properties. The improved bounds lower the number of Scenarios required for these problems, leading both to lower objective value and reduced computational complexity. The efficacy of the proposed bound is demonstrated on an inventory management example, and is in general applicable to randomized Model Predictive Control of chance constrained linear systems with additive uncertain input.
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on the connection between compression learning and Scenario based single stage and cascading optimization problems
IEEE Transactions on Automatic Control, 2015Co-Authors: Kostas Margellos, Maria Prandini, John LygerosAbstract:We investigate the connections between compression learning and Scenario based optimization. We first show how to strengthen, or relax the consistency assumption at the basis of compression learning and provide novel learnability conditions for the underlying algorithms. We then consider different constrained optimization problems affected by uncertainty represented by means of Scenarios. We show that the compression learning perspective provides a unifying framework for Scenario based optimization, since the issue of providing guarantees on the probability of constraint violation reduces to a learning problem for an appropriately chosen algorithm that satisfies some consistency assumption. To illustrate this, we revisit the Scenario Approach within the developed context. Moreover, using the compression learning machinery we provide novel results on the probability of constraint violation for the class of cascading optimization problems.
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performance bounds for the Scenario Approach and an extension to a class of non convex programs
IEEE Transactions on Automatic Control, 2015Co-Authors: Peyman Mohajerin Esfahani, Tobias Sutter, John LygerosAbstract:We consider the Scenario Convex Program (SCP) for two classes of optimization problems that are not tractable in general: Robust Convex Programs (RCPs) and Chance-Constrained Programs (CCPs). We establish a probabilistic bridge from the optimal value of SCP to the optimal values of RCP and CCP in which the uncertainty takes values in a general, possibly infinite dimensional, metric space. We then extend our results to a certain class of non-convex problems that includes, for example, binary decision variables. In the process, we also settle a measurability issue for a general class of Scenario programs, which to date has been addressed by an assumption. Finally, we demonstrate the applicability of our results on a benchmark problem and a problem in fault detection and isolation.
Behcet Acikmeșe - One of the best experts on this subject based on the ideXlab platform.
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approximate convex hull based Scenario truncation for chance constrained trajectory optimization
Automatica, 2020Co-Authors: Hossein Sartipizadeh, Behcet AcikmeșeAbstract:Abstract In this paper, we study chance constrained trajectory optimization of linear systems with general ellipsoidal and polytopic state-input constraints where the constraints must be met with some prescribed confidence level. We use the sampling techniques, specifically Scenario Approach, due to their generality and tractability compared to the analytical methods. To address the main drawback of Scenario Approach, which may require large number of samples, we introduce an approximate convex hull-based method to significantly reduce the number of samples. Based on the allowable computational complexity, the prominent samples are selected in a proper mapping and the rest are truncated. The truncation error is later compensated for by adjusting (buffering) the constraint set, so that the satisfaction of constraints with the desired confidence level is still guaranteed. Simulation results confirm the theoretical predictions with solid performance of the proposed method after discarding about 99% of samples from the Scenario Approach, which remarkably speeds up the online computations.
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approximate convex hull based sample truncation for Scenario Approach to chance constrained trajectory optimization
Advances in Computing and Communications, 2018Co-Authors: Hossein Sartipizadeh, Behcet AcikmeșeAbstract:This paper proposes a new sampling-based method, utilizing approximate convex hulls, to chance constrained trajectory optimization. Chance constrained trajectory optimization formulations can be utilized in many autonomous control applications and is also a key component of stochastic model predictive control. Among different solution techniques proposed in the literature, sampling based methods have been widely utilized. These methods convert the stochastic optimization problem to a deterministic one with finite number of constraints by replacing the uncertain stochastic variable with a set of random samples, also called Scenarios. Unfortunately, large number of samples needed even after removing redundant ones is a complicating factor and imposes a high computational complexity. In this paper, we consider chance constrained trajectory optimization problems for linear systems with stochastic disturbances and polytopic feasible control and state sets. We present a strategy to significantly reduce the number of required samples by truncating them, in addition to removing redundancies. An $\epsilon$ -approximate convex hull is generated to truncate the samples, obtained by using systematic methods of the Scenario Approach to cover a prescribed probability mass with a prescribed level of confidence. Hence the real uncertainty region is inner approximated by the remaining samples. The truncation error is later compensated by adjusting, buffering, the supporting hyperplanes of the polytope accordingly. This deterministic characterization of stochastic disturbances allow us to reformulate the stochastic optimization problem with an approximate deterministic one. Hence the proposed Approach aims to reduce the computational complexity due to using a sampling, while balancing the conservatism introduced due to this approximation. Simulation results also confirm noncon-servative performance obtained by the proposed method after discarding about 99% of samples from the Scenario Approach, which remarkably speeds up the online computations.
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sample truncation for Scenario Approach to closed loop chance constrained trajectory optimization for linear systems
arXiv: Optimization and Control, 2018Co-Authors: Hossein Sartipizadeh, Behcet AcikmeșeAbstract:This paper studies closed-loop chance constrained control problems with disturbance feedback (equivalently state feedback) where state and input vectors must remain in a prescribed polytopic safe region with a predefined confidence level. We propose to use a Scenario Approach where the uncertainty is replaced with a set of random samples (Scenarios). Though a standard form of Scenario Approach is applicable in principle, it typically requires a large number of samples to ensure the required confidence levels. To resolve this drawback, we propose a method to reduce the computational complexity by eliminating the redundant samples and, more importantly, by truncating the less informative samples. Unlike the prior methods that start from the full sample set and remove the less informative samples at each step, we sort the samples in a descending order by first finding the most dominant ones. In this process the importance of each sample is measured via a proper mapping. Then the most dominant samples can be selected based on the allowable computational complexity and the rest of the samples are truncated offline. The truncation error is later compensated for by adjusting the safe regions via properly designed buffers, whose sizes are functions of the feedback gain and the truncation error.
George Wright - One of the best experts on this subject based on the ideXlab platform.
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promoting articulated action from diverse stakeholders in response to public policy Scenarios a case analysis of the use of Scenario improvisation method
QUT Business School, 2016Co-Authors: George Cairns, George Wright, Peter FairbrotherAbstract:In this paper we present a novel application of Scenario methods to engage a diverse constituency of senior stakeholders, with limited time availability, in debate to inform planning and policy development. Our case study project explores post-carbon futures for the Latrobe Valley region of the Australian state of Victoria. Our Approach involved initial deductive development of two ‘extreme Scenarios’ by a multi-disciplinary research team, based upon an extensive research programme. Over four workshops with the stakeholder constituency, these initial Scenarios were discussed, challenged, refined and expanded through an inductive process, whereby participants took ‘ownership’ of a final set of three Scenarios. These were both comfortable and challenging to them. The outcomes of this process subsequently informed public policy development for the region. Whilst this process did not follow a single extant structured, multi-stage Scenario Approach, neither was it devoid of form. Here, we seek to theorise and codify elements of our process – which we term ‘Scenario improvisation’ – such that others may adopt it.
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Scenario method and stakeholder engagement critical reflections on a climate change Scenarios case study
QUT Business School, 2013Co-Authors: George Cairns, Iftekhar Ahmed, Jane Mullett, George WrightAbstract:Scenario method is presented in the literature as a means for engaging heterogeneous stakeholder groups to explore climate change futures and to inform policy and planning for adaptation responses. We discuss a case study project investigating possible interactions between climate change impacts and a proposed major port expansion in Australia. The study engaged participants from the private sector, government and environmental groups, with input from college students from the local area. Semi-structured interviews and a Scenario workshop were employed, creating individual space for expression of ideas, then a collaborative space for sharing these, exploring differences of perception and meaning, and developing a set of possible and plausible Scenarios. Whilst the workshop resulted in consensus on key issues and proposed actions, intended to inform policy formation and planning, there was an unforeseen lack of short term follow up and of the groups working more closely together. We discuss the reasons for this through reflective critical analysis of both our own process and of contingent factors in the wider contextual environment. We conclude that the basic Scenario Approach is valuable, but does not itself act as a catalyst for effecting change when multiple agencies, interests and agendas and strong contingent factors are present. © 2012 Elsevier Inc.
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Scenario method and stakeholder engagement critical reflections on a climate change Scenarios case study
Technological Forecasting and Social Change, 2013Co-Authors: George Cairns, Iftekhar Ahmed, Jane Mullett, George WrightAbstract:Scenario method is presented in the literature as a means for engaging heterogeneous stakeholder groups to explore climate change futures and to inform policy and planning for adaptation responses. We discuss a case study project investigating possible interactions between climate change impacts and a proposed major port expansion in Australia. The study engaged participants from the private sector, government and environmental groups, with input from college students from the local area. Semi-structured interviews and a Scenario workshop were employed, creating individual space for expression of ideas, then a collaborative space for sharing these, exploring differences of perception and meaning, and developing a set of possible and plausible Scenarios. Whilst the workshop resulted in consensus on key issues and proposed actions, intended to inform policy formation and planning, there was an unforeseen lack of short term follow up and of the groups working more closely together. We discuss the reasons for this through reflective critical analysis of both our own process and of contingent factors in the wider contextual environment. We conclude that the basic Scenario Approach is valuable, but does not itself act as a catalyst for effecting change when multiple agencies, interests and agendas and strong contingent factors are present.
Kostas Margellos - One of the best experts on this subject based on the ideXlab platform.
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a Scenario Approach for non convex control design
IEEE Transactions on Automatic Control, 2016Co-Authors: Sergio Grammatico, Kostas Margellos, Xiaojing Zhang, Paul J Goulart, John LygerosAbstract:Randomized optimization is an established tool for control design with modulated robustness. While for uncertain convex programs there exist efficient randomized Approaches, this is not the case for non-convex problems. Methods based on statistical learning theory are applicable to non-convex problems, but they usually are conservative in achieving the desired probabilistic guarantees. In this paper, we derive a novel Scenario Approach for a wide class of random non-convex programs, with a sample complexity similar to that of uncertain convex programs and with probabilistic guarantees that hold not only for the optimal solution of the Scenario program, but for all feasible solutions inside a set of a-priori chosen complexity. We also address measure-theoretic issues for uncertain convex and non-convex programs. Among the family of non-convex control-design problems that can be addressed via randomization, we apply our Scenario Approach to stochastic model predictive control for chance constrained nonlinear control-affine systems.
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on the connection between compression learning and Scenario based single stage and cascading optimization problems
IEEE Transactions on Automatic Control, 2015Co-Authors: Kostas Margellos, Maria Prandini, John LygerosAbstract:We investigate the connections between compression learning and Scenario based optimization. We first show how to strengthen, or relax the consistency assumption at the basis of compression learning and provide novel learnability conditions for the underlying algorithms. We then consider different constrained optimization problems affected by uncertainty represented by means of Scenarios. We show that the compression learning perspective provides a unifying framework for Scenario based optimization, since the issue of providing guarantees on the probability of constraint violation reduces to a learning problem for an appropriately chosen algorithm that satisfies some consistency assumption. To illustrate this, we revisit the Scenario Approach within the developed context. Moreover, using the compression learning machinery we provide novel results on the probability of constraint violation for the class of cascading optimization problems.
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on the road between robust optimization and the Scenario Approach for chance constrained optimization problems
IEEE Transactions on Automatic Control, 2014Co-Authors: Kostas Margellos, Paul J Goulart, John LygerosAbstract:We propose a new method for solving chance constrained optimization problems that lies between robust optimization and Scenario-based methods. Our method does not require prior knowledge of the underlying probability distribution as in robust optimization methods, nor is it based entirely on randomization as in the Scenario Approach. It instead involves solving a robust optimization problem with bounded uncertainty, where the uncertainty bounds are randomized and are computed using the Scenario Approach. To guarantee that the resulting robust problem is solvable we impose certain assumptions on the dependency of the constraint functions with respect to the uncertainty and show that tractability is ensured for a wide class of systems. Our results lead immediately to guidelines under which the proposed methodology or the Scenario Approach is preferable in terms of providing less conservative guarantees or reducing the computational cost.
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a Scenario Approach for non convex control design
arXiv: Systems and Control, 2014Co-Authors: Sergio Grammatico, Kostas Margellos, Xiaojing Zhang, Paul J Goulart, John LygerosAbstract:Randomized optimization is an established tool for control design with modulated robustness. While for uncertain convex programs there exist randomized Approaches with efficient sampling, this is not the case for non-convex problems. Approaches based on statistical learning theory are applicable to non-convex problems, but they usually are conservative in terms of performance and require high sample complexity to achieve the desired probabilistic guarantees. In this paper, we derive a novel Scenario Approach for a wide class of random non-convex programs, with a sample complexity similar to that of uncertain convex programs and with probabilistic guarantees that hold not only for the optimal solution of the Scenario program, but for all feasible solutions inside a set of a-priori chosen complexity. We also address measure-theoretic issues for uncertain convex and non-convex programs. Among the family of non-convex control- design problems that can be addressed via randomization, we apply our Scenario Approach to randomized Model Predictive Control for chance-constrained nonlinear control-affine systems.
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probabilistic guarantees for the n 1 security of systems with wind power generation
Reliability and risk evaluation of wind integrated power systems, 2013Co-Authors: Maria Vrakopoulou, Kostas Margellos, John Lygeros, Goran AnderssonAbstract:We propose a novel framework for designing an N-1 secure generation day-ahead dispatch for power systems with a high penetration of fluctuating power sources, e.g., wind or PV power. To achieve this, we integrate the security constraints in a DC optimal power flow optimization and formulate a stochastic program with chance constraints, which encode the probability of satisfying the transmission capacity constraints of the lines and the generation limits. To solve the resulting problem numerically, we transform the initial problem to a tractable one by using the so-called Scenario Approach, which is based on sampling the uncertain parameter while keeping the desired probabilistic guarantees. To generate wind power Scenarios a Markov chain-based model is employed. To illustrate the effectiveness of the proposed technique we apply it to the IEEE 30-bus network, and compare it with the solution of a deterministic variant of the problem, where the operator determines a secure generation dispatch based only on the available wind power forecast. A Monte Carlo simulation study is conducted to collect statistical results regarding the performance of our method.
Paul J Goulart - One of the best experts on this subject based on the ideXlab platform.
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a Scenario Approach for non convex control design
IEEE Transactions on Automatic Control, 2016Co-Authors: Sergio Grammatico, Kostas Margellos, Xiaojing Zhang, Paul J Goulart, John LygerosAbstract:Randomized optimization is an established tool for control design with modulated robustness. While for uncertain convex programs there exist efficient randomized Approaches, this is not the case for non-convex problems. Methods based on statistical learning theory are applicable to non-convex problems, but they usually are conservative in achieving the desired probabilistic guarantees. In this paper, we derive a novel Scenario Approach for a wide class of random non-convex programs, with a sample complexity similar to that of uncertain convex programs and with probabilistic guarantees that hold not only for the optimal solution of the Scenario program, but for all feasible solutions inside a set of a-priori chosen complexity. We also address measure-theoretic issues for uncertain convex and non-convex programs. Among the family of non-convex control-design problems that can be addressed via randomization, we apply our Scenario Approach to stochastic model predictive control for chance constrained nonlinear control-affine systems.
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on the sample size of random convex programs with structured dependence on the uncertainty
Automatica, 2015Co-Authors: Xiaojing Zhang, Sergio Grammatico, Paul J Goulart, Georg Schildbach, John LygerosAbstract:The “Scenario Approach” provides an intuitive method to address chance constrained problems arising in control design for uncertain systems. It addresses these problems by replacing the chance constraint with a finite number of sampled constraints (Scenarios). The sample size critically depends on Helly’s dimension, a quantity always upper bounded by the number of decision variables. However, this standard bound can lead to computationally expensive programs whose solutions are conservative in terms of cost and violation probability. We derive improved bounds of Helly’s dimension for problems where the chance constraint has certain structural properties. The improved bounds lower the number of Scenarios required for these problems, leading both to improved objective value and reduced computational complexity. Our results are generally applicable to Randomized Model Predictive Control of chance constrained linear systems with additive uncertainty and affine disturbance feedback.
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on the sample size of random convex programs with structured dependence on the uncertainty
arXiv: Optimization and Control, 2015Co-Authors: Xiaojing Zhang, Sergio Grammatico, Paul J Goulart, Georg Schildbach, John LygerosAbstract:Many control design problems subject to uncertainty can be cast as chance constrained optimization programs. The Scenario Approach provides an intuitive way to address these problems by replacing the chance constraint with a finite number of sampled constraints (Scenarios). The sample size critically depends on the so-called Helly's dimension, which is always upper bounded by the number of decision variables. However, this standard bound can lead to computationally expensive programs whose solutions are conservative in terms of cost/violation probability. This paper derives improved bounds of Helly's dimension for problems where the chance constraint has certain structural properties. The improved bounds lower the number of Scenarios required for these problems, leading both to lower objective value and reduced computational complexity. The efficacy of the proposed bound is demonstrated on an inventory management example, and is in general applicable to randomized Model Predictive Control of chance constrained linear systems with additive uncertain input.
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on the road between robust optimization and the Scenario Approach for chance constrained optimization problems
IEEE Transactions on Automatic Control, 2014Co-Authors: Kostas Margellos, Paul J Goulart, John LygerosAbstract:We propose a new method for solving chance constrained optimization problems that lies between robust optimization and Scenario-based methods. Our method does not require prior knowledge of the underlying probability distribution as in robust optimization methods, nor is it based entirely on randomization as in the Scenario Approach. It instead involves solving a robust optimization problem with bounded uncertainty, where the uncertainty bounds are randomized and are computed using the Scenario Approach. To guarantee that the resulting robust problem is solvable we impose certain assumptions on the dependency of the constraint functions with respect to the uncertainty and show that tractability is ensured for a wide class of systems. Our results lead immediately to guidelines under which the proposed methodology or the Scenario Approach is preferable in terms of providing less conservative guarantees or reducing the computational cost.
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a Scenario Approach for non convex control design
arXiv: Systems and Control, 2014Co-Authors: Sergio Grammatico, Kostas Margellos, Xiaojing Zhang, Paul J Goulart, John LygerosAbstract:Randomized optimization is an established tool for control design with modulated robustness. While for uncertain convex programs there exist randomized Approaches with efficient sampling, this is not the case for non-convex problems. Approaches based on statistical learning theory are applicable to non-convex problems, but they usually are conservative in terms of performance and require high sample complexity to achieve the desired probabilistic guarantees. In this paper, we derive a novel Scenario Approach for a wide class of random non-convex programs, with a sample complexity similar to that of uncertain convex programs and with probabilistic guarantees that hold not only for the optimal solution of the Scenario program, but for all feasible solutions inside a set of a-priori chosen complexity. We also address measure-theoretic issues for uncertain convex and non-convex programs. Among the family of non-convex control- design problems that can be addressed via randomization, we apply our Scenario Approach to randomized Model Predictive Control for chance-constrained nonlinear control-affine systems.
